A370202 a(n) = a(n-3) + a(n-2) + gcd(a(n-2), a(n-1)) with a(1) = a(2) = a(3) = 1.

1, 1, 1, 3, 3, 7, 7, 17, 15, 25, 37, 41, 63, 79, 105, 143, 185, 249, 329, 435, 579, 767, 1015, 1347, 1783, 2363, 3131, 4147, 5495, 7279, 9643, 12775, 16923, 22419, 29701, 39343, 52121, 69045, 91465, 121171, 160511, 212637, 281683, 373149, 494321, 654833, 867471

Offset

1,4

Comments

The ratio between consecutive terms (a(n)/a(n-1)) appears to approach the plastic constant A060006.

Links

Eli Jaffe, Table of n, a(n) for n = 1..1000

Prog

(Python)
from math import gcd
def terms(n):
  nums = [1, 1, 1]
  for i in range(n-3):
    new_num = nums[i] + nums[i+1] + gcd(nums[i+1], nums[i+2])
    nums.append(new_num)
  return nums

Crossrefs

Cf. A060006, A083658.

Sequence in context: A233810 A263869 A174583 * A226781 A147144 A152113

Adjacent sequences: A370199 A370200 A370201 * A370203 A370204 A370205

Keyword

nonn,easy

Author

Eli Jaffe, Feb 11 2024

Status

approved